Feasibility study for the measurement of the angular asymmetry in the production of a bottom quark-antiquark pair in electron-positron collisions with a center-of-mass energy of 91 GeV at the future accelerator FCC-ee at CERN

The Standard Model (SM) of particle physics has proved to be an extremely successful theory of elementary interactions, and its predictions have been tested up to the per-mill level by a wide variety of measurements. On the other hand, several experimental facts require the extension of the Standard Model and explanations are needed for observations such as the domination of matter over antimatter, the evidence for \emph{dark matter} and the non-zero neutrino masses. Theoretical issues that need to be addressed include the \emph{hierarchy problem}, the neutrality of the Universe, the stability of the Higgs boson mass upon quantum corrections and the \emph{strong CP problem}.

Global fits to electroweak precision data, comparing the measured values of different quantities with the SM predictions, provide important checks of the SM consistency and sensitivity to beyond-the-SM (BSM) effects. The two most sensitive determinations of $\sin^2\theta_{\rm W,eff}$, from the LEP measurement of the $b$-quark production forward-backward asymmetry at the $Z$-boson mass pole $A^{0,b}_{FB}$, and from the SLD measurement of $A_\ell$, are in $\sim$3 $\sigma$ tension with each other, constituting the largest deviation in global electroweak fits.

This issue has remained unsolved for the past 25 years, as documented by the flourishing literature regarding its possible nature. Possible BSM explanations would require a sizable correction to the right-handed $Zb\bar{b}$ coupling, keeping the left-handed $Zb\bar{b}$ coupling unchanged.

To shed light on this discrepancy, it is thus essential to exclude the possibility that it was caused by a statistical fluctuation or, even if almost excluded by dedicated studies, by some subtle underestimation of systematic experimental uncertainties. In both cases, it is clear that a new experimental, even indirect, determination of $A^{0,b}_{FB}$ is quite urgent.

This thesis belongs to the context of research for new physics in the electroweak sector at $Z$-pole, and consists in the presentation of a feasibility study on the measurement of an asymmetry, $A^{0,b}_{FB}$, in the associated production of a bottom quark-antiquark pair coming from a decaying $Z$-boson, at the future collider FCC-ee. This provides a clean observable, which is affected by hadronic uncertainties of both experimental and theoretical origin.

The definition of this asymmetry intrinsically requires some sensitivity to the charge of the bottom quark/antiquark in the final state, which represents an important experimental challenge.

By means of a fast-simulation based study, with the generation of samples of signal and background events from electron-positron collisions at the center-of-mass energy of $91\,\textup{GeV}$, a simple technique for the $b$-quark charge identification is investigated, relying on charged particle tracks within the cone of the hadronic jet resulting from the its fragmentation process.

The directions of the reconstructed hadronic jets, together with the information on their identified charge, are then used to build the final observable. A simple unfolding technique is then implemented, and pseudo-experiments based on simulated data are performed in order to estimate the expected statistical uncertainty and the main sources of systematic uncertainty in the proposed measurement.

The first projections for an $A^{{\rm 0},b}_{FB}$ measurement at the FCC-ee are then reported, indicating the possibility of significantly improving on the current precision of the measurement performed at LEP.